The inapproximability of non NP-hard optimization problems

Abstract

The inapproximability of non NP-hard optimization problems is investigated. Based on self-reducibility and approximation preserving reductions, it is shown that problems LOG DOMINATING SET, TOURNAMENT DOMINATING SET and RICH HYPERGRAPH VERTEX COVER cannot be approximated to a constant ratio in polynomial time unless the corresponding NP-hard versions are also approximable in deterministic subexponential time. A direct connection is established between non NP-hard problems and a PCP characterization of NP. Reductions from the PCP characterization show that LOG CLIQUE is not approximable in polynomial time and MAX SPARSE SAT does not have a PTAS under the assumption that SAT cannot be solved in deterministic 2O(log n√n) time and that NP ⊈ DTIME(2o(n)). © Springer-Verlag Berlin Heidelberg 1998.